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# Investments - Math Problem Example

Summary to math problem on topic "Investments"
(b) As we can see from the equation used the Sharpe portfolio performance measure uses the standard deviation of returns as the measure of total risk, whereas the Treynor's performance measure uses beta (systematic risk). The Sharpe measure, therefore, evaluates the portfolio manager on the basis of both rate of return performance and diversification whereas the Treynor's evaluates the portfolio manager on the basis of systematic risk.

## Extract of math problem "Investments"

If any on do it nicely he/she can identify a better stock for investment to make lot of money. But these identification and estimation is itself a tough task.
Part C:
If we talk about portfolio risk options trading looks a lot more versatile than futures trading and the main reason behind it is a profit in all direction can be created by using option strategies.
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But if we look at the future trading it is single directional that is the direction of money id directly proportional to the direction of the stock price.
So we can say that futures' trading is one of the important risk management tool and at the same time a speculative technique whereas options' trading involves a strategic investment on its own. Hence we can say that both trading instruments can place themselves in every well diversified portfolio for the investor.

Question 5: Part A:
As we know that,
According to CAPM,

Where,
R(i)=Expected rate of return
R(f)= Risk free rate of return
R(m)= Market rate of return
=beta
So,

Hence the expected rate of return=12%
(b) Answer: The expected rate of return with =0 is equals to the risk free rate of return.
According to CAPM,

Now as the share will be sold of after 1 year,
Value of share price after one year=\$41
Expected dividend=\$3
Hence,

Hence the share is underpriced.

Part B:

As we can see from the graph here the x-axis represents the portfolio return and the y-axis represents the risk factor. Portfolio can't be expected above this efficient frontier line. At the lower level we can see that a low risk represents lower return, medium risk medium return and high risk high return.

Question 6: Part A
As we know that:

So,

If we talk about portfolio risk options trading looks a lot more versatile than futures trading and the main reason behind it is a profit in all direction can be created by using option strategies. But if we look at the future trading it is single directional that is the direction of money id directly proportional to the direction of the stock price.
So we can say that futures' trading is one of the important risk management tool and at the same time a speculative technique whereas options' trading involves a strategic investment on its own. Hence we can say that both trading instruments can place themselves in every well diversified portfolio for the investor.
As we can see from the graph here the x-axis represents the portfolio return and the y-axis represents the risk factor. Portfolio can't be expected above this efficient frontier line. At the lower level we can see that a low risk represents lower return, medium risk medium return and high risk high return.
Supportive argument: The manager performance only reflects in the return of the portfolio. i.e. when manager perform well the portfolio will also perform well. ...Download file "Investments" to see next pagesRead More
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